Avogadro's Law derivation

[Arnav]

How did Avogadro 'actually' derive his law stating "equal volumes of gases under similar conditions of temperature and pressure contain same number of molecules" ?

I am a 10th grader so I would appreciate a lucid and intuitive explain if the derivation involves higher concepts of science.

[swansont]

I think he saw a trend in experimental results (his paper is listed in the footnotes here https://en.wikipedia.org/wiki/Avogadro's_law and there's an English translation in #2)

It's also true that his work was after the formulation of Boyle's law, PV = constant (1662), Charles's law, V/T = constant (1787) and Gay-Lussac's law, P/T is constant (1808)

So it seems he was extrapolating that these laws are all dependent on the number of atoms in the sample being constant, and the variables would vary in proportion if you changed the number of molecules.

[studiot]

1 hour ago, Arnav said:

How did Avogadro 'actually' derive his law stating "equal volumes of gases under similar conditions of temperature and pressure contain same number of molecules" ?

I am a 10th grader so I would appreciate a lucid and intuitive explain if the derivation involves higher concepts of science.

Interesting question as today we derive Avogadro's Hypothesis (as it was originally called) from the kinetic theory following Maxwell's theoretical derivation.

Avogadro himself used a different route.
He was concerned with chemical reactions between gasses and explaining the simple relationship between the volumes of gasses entering into chemical combination.
Note he said molecules, not atoms.

He suggested that the densities of these reacting gasses, under the same conditions of temperature and pressure are in the ratios of their respective masses of their molecules.
From this it follows that they are in the same ratios as their molecular masses (then called molecular weights).
Since these are all relative to a standard gas (eg taking oxygen as 16) the hypothesis follows for equal volumes.

 

[Arnav]

 

4 hours ago, swansont said:

I think he saw a trend in experimental results (his paper is listed in the footnotes here https://en.wikipedia.org/wiki/Avogadro's_law and there's an English translation in #2)

It's also true that his work was after the formulation of Boyle's law, PV = constant (1662), Charles's law, V/T = constant (1787) and Gay-Lussac's law, P/T is constant (1808)

So it seems he was extrapolating that these laws are all dependent on the number of atoms in the sample being constant, and the variables would vary in proportion if you changed the number of molecules.

Thanks swansont for the paper, but I lost it at the caloric thing😅

 

 

Studiot, how did Avogadro conclude that the ratio of the volumes of two gases under similar conditions was equal to the ratio of their molecular weights? Sorry if I sound too dumb

[studiot]

3 hours ago, Arnav said:

Studiot, how did Avogadro conclude that the ratio of the volumes of two gases under similar conditions was equal to the ratio of their molecular weights? Sorry if I sound too dumb

This is a question of Chemistry, not Physics.

In order to understand what was going on at that time it is necessary to know that Avogadro was contradicting two Scientists who Wikipedia label as the founders of modern Chemistry,

Dalton and Berzelius.

They were proponents of Dalton's atomic theory did not acknowledge molecules, but held that in a chemical reaction one atom of A combined with one atom of B to give one atom of C.

Dalton and Berzelius made great advances in chemistry but they did not accept molecules so when Avogardro made his hypothesis they fought tooth and nail against and as the great men of their day, this held back progress for nearly half a century.
Note Avogadro did not call his hypothesis a Law, but merely stated that if solved the apparent problem of measuring chemical composition by volume.

He starts his paper thus (English translation)

Quote

Avogadro

M. Gay-Lussac has shown in an interesting memoir that gases always unite in a very simple proportion by volume, and that when the result of their union is a gas, its volume is also simply related to those of its components.

In turn Gay Lussac had written from experimental evidence

Quote

Gay-Lussac

When gases combine together at constant temperature and pressure they do so in volumes which bear a simple ratio to each other and to the volume of the product if gaseous.

 

Now it was known that

I volume of hydrogen + 1 volume of chlorine yields 2 volumes of hydrogen chloride.

Dalton proposed that each volume of reactant and product contained the same number of atoms of their respective gases so

n atoms of hydrogen + n atoms of chlorine yield 2n particles of hydrogen chloride.

1 atom of hydrogen + 1 atom of chlorine yield 2 particles of hydrogen chloride.

But each particle of hydrogen chloride must contain some hydrogen and some chlorine.

So the only way this can be true is if the atoms split into parts, which is contrary to Daltons definition of an atom as the smallest indivisible particle.

The same difficulty was encountered with other known gaseous reactions such as hydrogen and oxygen, hydrogen and nitrogen, oxygen and nitrogen.

Avogadro's paper proposes that if in some gases  atoms are joined together into larger particles, containing two or more atoms such that these larger particles, he called molecules, are substituted for atoms in Dalton's proposal Gay-Lussac's Law is automatically satisfied for both reactants and products. He then makes his famous hypothesis

Quote

Avogadro

Equal volumes of all gases at the same temperature and pressure contain the same number of molecules

He also states that following this hypothesis : the ratio of the weights of equal volumes of two gases A and B must be the same as the ratio of the weight  1 molecule of A to 1 molecules of B.

The job was not completed until 1858 by Cannizzaro who extended this to atomic masses.

Not sure why so are so deeply interested (but I am pleased someone is).

The really important thing Avogadro 'discovered' was the molecule as distinct from the atom and linked this to the connection between weight and volume.

There is a really good book about all this by a top notch Chemist called

Chasing the Molecule

John Buckingham

Which is the history (with good scientific explanations) of molecules and chemical formulae in general.